Question 2
In a competition, there are $a$ contestants and $b$ judges, where $b \ge 3$ is an odd integer. Each judge rates each contestant as either “pass” or “fail”. Suppose $k$ is a number such that for any two judges, their ratings coincide for at most $k$ contestants. Prove that $$
\frac ka \ge \frac{b-1}{2b}.
$$
\frac ka \ge \frac{b-1}{2b}.
$$